Elementary Topology

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Elementary Topology

O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
Elementary Topology Book PDF

Author : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
Publisher : American Mathematical Soc.
Page : 432 pages
File Size : 51,7 Mb
Release : 2024-06-11
Category : Mathematics
ISBN : 0821886258

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Elementary Topology by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov Pdf

This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.

Elementary Applied Topology

Robert W. Ghrist
Elementary Applied Topology Book PDF

Author : Robert W. Ghrist
Publisher : Createspace Independent Publishing Platform
Page : 0 pages
File Size : 52,6 Mb
Release : 2014
Category : Mathematics
ISBN : 1502880857

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Elementary Applied Topology by Robert W. Ghrist Pdf

This book gives an introduction to the mathematics and applications comprising the new field of applied topology. The elements of this subject are surveyed in the context of applications drawn from the biological, economic, engineering, physical, and statistical sciences.

Elementary Concepts of Topology

Paul Alexandroff
Elementary Concepts of Topology Book PDF

Author : Paul Alexandroff
Publisher : Courier Corporation
Page : 68 pages
File Size : 44,6 Mb
Release : 2012-08-13
Category : Mathematics
ISBN : 9780486155067

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Elementary Concepts of Topology by Paul Alexandroff Pdf

Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.

Elementary Topology

Michael C. Gemignani
Elementary Topology Book PDF

Author : Michael C. Gemignani
Publisher : Courier Corporation
Page : 292 pages
File Size : 40,6 Mb
Release : 1990-01-01
Category : Mathematics
ISBN : 0486665224

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Elementary Topology by Michael C. Gemignani Pdf

Topology is one of the most rapidly expanding areas of mathematical thought: while its roots are in geometry and analysis, topology now serves as a powerful tool in almost every sphere of mathematical study. This book is intended as a first text in topology, accessible to readers with at least three semesters of a calculus and analytic geometry sequence. In addition to superb coverage of the fundamentals of metric spaces, topologies, convergence, compactness, connectedness, homotopy theory, and other essentials, Elementary Topology gives added perspective as the author demonstrates how abstract topological notions developed from classical mathematics. For this second edition, numerous exercises have been added as well as a section dealing with paracompactness and complete regularity. The Appendix on infinite products has been extended to include the general Tychonoff theorem; a proof of the Tychonoff theorem which does not depend on the theory of convergence has also been added in Chapter 7.

Intuitive Concepts in Elementary Topology

B.H. Arnold
Intuitive Concepts in Elementary Topology Book PDF

Author : B.H. Arnold
Publisher : Courier Corporation
Page : 192 pages
File Size : 43,7 Mb
Release : 2015-02-23
Category : Mathematics
ISBN : 9780486275765

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Intuitive Concepts in Elementary Topology by B.H. Arnold Pdf

Classroom-tested and much-cited, this concise text is designed for undergraduates. It offers a valuable and instructive introduction to the basic concepts of topology, taking an intuitive rather than an axiomatic viewpoint. 1962 edition.

Lecture Notes on Elementary Topology and Geometry

I.M. Singer,J.A. Thorpe
Lecture Notes on Elementary Topology and Geometry Book PDF

Author : I.M. Singer,J.A. Thorpe
Publisher : Springer
Page : 240 pages
File Size : 46,9 Mb
Release : 2015-05-28
Category : Mathematics
ISBN : 9781461573470

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Lecture Notes on Elementary Topology and Geometry by I.M. Singer,J.A. Thorpe Pdf

At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis.

Elementary Topology And Applications (Second Edition)

Carlos R Borges
Elementary Topology And Applications Second Edition Book PDF

Author : Carlos R Borges
Publisher : World Scientific
Page : 174 pages
File Size : 55,9 Mb
Release : 2021-07-21
Category : Mathematics
ISBN : 9789811237447

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Elementary Topology And Applications (Second Edition) by Carlos R Borges Pdf

The textbook is a very good start into the mathematical field of topology. A variety of topological concepts with some elementary applications are introduced. It is organized in such a way that the reader gets to significant applications quickly.This revised version corrects the many discrepancies in the earlier edition. The emphasis is on the geometric understanding and the use of new concepts, indicating that topology is really the language of modern mathematics.

Elementary Topology

Donald W. Blackett
Elementary Topology Book PDF

Author : Donald W. Blackett
Publisher : Academic Press
Page : 236 pages
File Size : 43,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483262536

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Elementary Topology by Donald W. Blackett Pdf

Elementary Topology: A Combinatorial and Algebraic Approach focuses on the application of algebraic methods to topological concepts and theorems. The publication first elaborates on some examples of surfaces and their classifications. Discussions focus on combinatorial invariants of a surface, combinatorial equivalence, surfaces and their equations, topological surfaces, coordinates on a sphere and torus, and properties of the sphere and torus. The text then examines complex conics and covering surfaces and mappings into the sphere, including applications of the winding number in complex analysis, mappings into the plane, winding number of a plane curve, covering surfaces, and complex conies. The book examines vector fields, network topology, and three-dimensional topology. Topics include topological products and fiber bundles, manifolds of configurations, paths, circuits, and trees, vector fields and hydrodynamics, vector fields on a sphere, and vector fields and differential equations. The publication is highly recommended for sophomores, juniors, and seniors who have completed a year of calculus.

Topology

Tai-Danae Bradley,Tyler Bryson,John Terilla
Topology Book PDF

Author : Tai-Danae Bradley,Tyler Bryson,John Terilla
Publisher : MIT Press
Page : 167 pages
File Size : 55,9 Mb
Release : 2020-08-18
Category : Mathematics
ISBN : 9780262359627

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Topology by Tai-Danae Bradley,Tyler Bryson,John Terilla Pdf

A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.

Elementary Symplectic Topology and Mechanics

Franco Cardin
Elementary Symplectic Topology and Mechanics Book PDF

Author : Franco Cardin
Publisher : Springer
Page : 222 pages
File Size : 40,8 Mb
Release : 2014-12-01
Category : Science
ISBN : 9783319110264

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Elementary Symplectic Topology and Mechanics by Franco Cardin Pdf

This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. Following this line of thought, first introduced by Wlodemierz Tulczyjew, geometric solutions of Hamilton-Jacobi equations, Hamiltonian vector fields and canonical transformations are described by suitable Lagrangian submanifolds belonging to distinct well-defined symplectic structures. This unified point of view has been particularly fruitful in symplectic topology, which is the modern Hamiltonian environment for the calculus of variations, yielding sharp sufficient existence conditions. This line of investigation was initiated by Claude Viterbo in 1992; here, some primary consequences of this theory are exposed in Chapter 8: aspects of Poincaré's last geometric theorem and the Arnol'd conjecture are introduced. In Chapter 7 elements of the global asymptotic treatment of the highly oscillating integrals for the Schrödinger equation are discussed: as is well known, this eventually leads to the theory of Fourier Integral Operators. This short handbook is directed toward graduate students in Mathematics and Physics and to all those who desire a quick introduction to these beautiful subjects.

Elementary Topology

Guilford Spencer,Karo Maestro,Dick Hall
Elementary Topology Book PDF

Author : Guilford Spencer,Karo Maestro,Dick Hall
Publisher : Unknown
Page : 337 pages
File Size : 43,6 Mb
Release : 2019-01-10
Category : Electronic
ISBN : 1791574785

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Elementary Topology by Guilford Spencer,Karo Maestro,Dick Hall Pdf

This book is an introduction to point set topology for undergraduates. Many of the classic textbooks on the subject cover the subject exhaustively and at the highest possible level of generality. The result of using traditional textbooks has been that students spend 2 semesters learning far more general topology on abstract spaces then most of them will ever need to use or know. More importantly, students get the impression from geometers and topologists in later courses that they "wasted" a year of their studies learning material that most mathematicians don't even consider topology anymore. This leaves many of them feeling deceived and frustrated. Unfortunately, the reaction has been in recent decades to write elementary topology textbooks that only present the barest minimum of point set topology needed for students in advanced geometry or algebraic topology. Indeed-some recent beginning textbooks in topology largely skip general topology altogether and jump straight into algebraic and geometric topology such as homotopy, curves and surfaces! We believe this ludicrous solution is essentially throwing the baby out with the bathwater. This reissued edition of Hall/ Spencer should seriously be considered by mathematicians as the benchmark for such a course. The book contains what we believe to be approximately the irreducible minimum of point set topology any student of mathematics needs to learn regardless of level or interest. The book is quite detailed, covering sufficient general topology of interest and use for analysts, geometers and topologists. The book falls into two rather distinct parts. The first half is concerned with an introductory study of topological and metric spaces. The basic operations with sets are introduced in Chapter I, relations and mappings are discussed, and an introduction to infinite and uncountable sets is given. Chapter 2 introduces the basic topological structure of the real numbers in a review of basic analysis. In Chapter 3, general topological and metric spaces are introduced and such topics as compactness, separation and continuous functions are discussed. Metric spaces are pursued further in Chapter 4, with discussions of local connectivity, countability, metrizability and completion being included. The second part is less elementary in character. The long Chapter 5 is concerned with giving topological characterizations of arcs, simple closed curves, and simple closed surfaces. Peano spaces are discussed and the Jordan curve theorem and Jordan-Schoenflies theorem are proved. Chapter 6 discusses partitionable spaces, a topic often missing from modern texts. Finally, Chapter 7 discusses the axiom of choice, Zorn's lemma (in the form commonly called the Hausdorff niaximality principle) and the Tychonoff product theorem. The book in particular will help students understand the deep connection between general topology and real and complex analysis. The most natural path towards understanding abstract topological spaces, general continuous mappings and topological invariants on families of open sets is to see how they directly generalize the usual structures of analysis on the real line. Also. Blue Collar Scholar founder/editor Karo Maestro has added his usual personal touch to the new edition, with a new preface on his own reflections on point set topology and recommendations for supplementary or subsequent study. The prerequisites for the text are very minimal-just calculus and some experience with rigorous proofs. This wonderful lost text in this new inexpensive edition will serve a new generation of mathematics students who need to learn this crucial foundational subject with a presentation that's both detailed and informative without being exhaustive. It will indoctrinate students into the beauty and simplicity of point-set topology and convince them of its' intrinsic importance-primarily to analysis, but also to other areas of mathematics.

Elementary Point-Set Topology

Andre L. Yandl,Adam Bowers
Elementary Point Set Topology Book PDF

Author : Andre L. Yandl,Adam Bowers
Publisher : Courier Dover Publications
Page : 256 pages
File Size : 43,6 Mb
Release : 2016-04-10
Category : Mathematics
ISBN : 9780486811017

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Elementary Point-Set Topology by Andre L. Yandl,Adam Bowers Pdf

In addition to serving as an introduction to the basics of point-set topology, this text bridges the gap between the elementary calculus sequence and higher-level mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and suitable for a variety of introductory courses. Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations. "This is a back-to-basics introductory text in point-set topology that can double as a transition to proofs course. The writing is very clear, not too concise or too wordy. Each section of the book ends with a large number of exercises. The optional first chapter covers set theory and proof methods; if the students already know this material you can start with Chapter 2 to present a straight topology course, otherwise the book can be used as an introduction to proofs course also." — Mathematical Association of America

Elementary Differential Topology

James R. Munkres
Elementary Differential Topology Book PDF

Author : James R. Munkres
Publisher : Princeton University Press
Page : 136 pages
File Size : 45,5 Mb
Release : 1966
Category : Mathematics
ISBN : 0691090939

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Elementary Differential Topology by James R. Munkres Pdf

Annotation The Description for this book, Elementary Differential Topology. (AM-54), will be forthcoming.

Elementary Topology

O. I͡A. Viro
Elementary Topology Book PDF

Author : O. I͡A. Viro
Publisher : American Mathematical Soc.
Page : 400 pages
File Size : 48,6 Mb
Release : 2008
Category : Mathematics
ISBN : 0821845063

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Elementary Topology by O. I͡A. Viro Pdf

"This textbook on elementary topologycontains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elernentary segment centered at the notions of fundamental group and covering space. The reader who has mastered the core material acquires a strong background in elementary topology and will feel at home in the environment of abstract mathemeatics."--BOOK JACKET.

Knots, Molecules, and the Universe

Erica Flapan
Knots Molecules and the Universe Book PDF

Author : Erica Flapan
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 40,5 Mb
Release : 2015-12-22
Category : Algebraic topology
ISBN : 9781470425357

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Knots, Molecules, and the Universe by Erica Flapan Pdf

This book is an elementary introduction to geometric topology and its applications to chemistry, molecular biology, and cosmology. It does not assume any mathematical or scientific background, sophistication, or even motivation to study mathematics. It is meant to be fun and engaging while drawing students in to learn about fundamental topological and geometric ideas. Though the book can be read and enjoyed by nonmathematicians, college students, or even eager high school students, it is intended to be used as an undergraduate textbook. The book is divided into three parts corresponding to the three areas referred to in the title. Part 1 develops techniques that enable two- and three-dimensional creatures to visualize possible shapes for their universe and to use topological and geometric properties to distinguish one such space from another. Part 2 is an introduction to knot theory with an emphasis on invariants. Part 3 presents applications of topology and geometry to molecular symmetries, DNA, and proteins. Each chapter ends with exercises that allow for better understanding of the material. The style of the book is informal and lively. Though all of the definitions and theorems are explicitly stated, they are given in an intuitive rather than a rigorous form, with several hundreds of figures illustrating the exposition. This allows students to develop intuition about topology and geometry without getting bogged down in technical details.